**Cube shape :**

A cube is a solid having six square faces. Example: Die.

The sum of the areas of all the six equal faces is called the Total Surface Area (T.S.A) of the cube.

In the figure given above, let the side of the cube measure a units. Then the area of each face of the cube is a^{2} square units.

Hence, the total surface area is 6a^{2} square units.

In a cube, if we don’t consider the top and bottom faces, the remaining area is called the Lateral Surface Area (L.S.A). Hence, the lateral surface area of the cube is 4a^{2} square units.

Let the side of a cube be a units. Then :

(i) The Total Surface Area (T.S.A) = 6a^{2} square units.

(ii) The Lateral Surface Area (L.S.A) = 4a^{2} square units.

If the side of a cube is a units, then its volume V is given by the formula

V = a^{3} cubic units

**Example 1 :**

Find the L.S.A, T.S.A and volume of a cube of side 5 cm.

**Solution :**

Lateral surface area (L.S.A) = 4a^{2}

= 4(52 ) = 100 sq. cm

Total surface area (T.S.A) = 6a^{2}

= 6 (5^{2} )

= 150 sq. cm

Volume of cube = a^{3}

= 5^{3}

= 125 cm^{3}

**Example 2 :**

Find the length of the side of a cube whose total surface area is 216 square cm.

**Solution :**

Let a be the side of the cube.

Given that T.S.A = 216 sq. cm

6a^{2} = 216

a^{2} = 216/6

a^{2} = 36

a = √36

a = 6 cm

**Example 3 :**

A cube has a total surface area of 384 sq. cm. Find its volume.

**Solution :**

Let a be the side of the cube. Given that T.S.A = 384 sq. cm

6a^{2} = 384

a^{2} = 384/6

a^{2} = 64

a = √64 = 8 cm

Hence, volume = a^{3} = 8^{3} = 512 cm^{3}

**Example 4 :**

If the lateral surface area of a cube is 900 cm^{2}, find the length of its side.

**Solution :**

Lateral surface area of cube = 4a^{2}

4a^{2 }= 900

a^{2 }= 900/4

a^{2 }= 225

a = √225

a = 15 cm

Hence the side of cube is 15 cm.

After having gone through the stuff given above, we hope that the students would have understood "Cube shape".

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